PSAT 8/9 cheat sheet

Main idea: the correct answer covers the whole passage, not one supporting detail; reject choices that are true but too narrow or too broad.

Command of evidence: quantitative choices must match the data in the stated direction (increase/decrease, greater/lesser) and use the correct comparison groups.

Words in context: substitute each choice into the sentence and keep the one whose connotation and register fit the surrounding text.

Transitions: classify the relationship between sentences first (contrast, cause, addition, example, sequence), then pick the matching transition word.

Boundaries: a period, semicolon, or colon can join independent clauses; a comma alone cannot create a sentence boundary error.

Nonessential elements: information set off by paired commas, dashes, or parentheses must be removable without breaking the sentence's grammar.

Subject-verb agreement: locate the true subject by crossing out prepositional phrases and parenthetical material before matching the verb.

Punctuation with lists and colons: a colon must follow an independent clause; items in a simple series are separated by commas with no comma before the final item unless the style requires it.

Slope: m = (y2 - y1)/(x2 - x1); parallel lines share m, perpendicular lines have slopes whose product is -1.

Linear form: y = mx + b, where m is the rate of change and b is the starting value; interpret both in context.

Systems: a system has no solution when the lines are parallel (same slope, different intercept), and infinitely many when the equations describe the same line.

Quadratics: for ax^2 + bx + c = 0, x = (-b +/- sqrt(b^2 - 4ac))/(2a); the discriminant b^2 - 4ac gives 2, 1, or 0 real solutions when positive, zero, or negative.

Exponent rules: x^a * x^b = x^(a+b), x^a / x^b = x^(a-b), (x^a)^b = x^(ab), and x^0 = 1 for nonzero x.

Percent change: percent change = (new - old)/old * 100; successive percent changes multiply rather than add.

Geometry: circle area = pir^2 and circumference = 2pi*r; triangle area = (1/2)bh; the Pythagorean theorem is a^2 + b^2 = c^2 for right triangles.

Statistics: mean = sum/count; median is the middle value of ordered data; range = max - min; adding a constant to every value shifts mean and median but not range or standard deviation.